Kamaji & Maths: The Power of Habit in Problem-Solving

In Charles Duhigg’s book, ‘The Power of Habit’, he lays out a compelling argument both for the powerful and simplicity of habits. They seem to happen without requiring any cognitive output, prompted by some unbeknownst thing working in the back of the mind; Kamaji, toiling in the boiler-room of the cerebellum. I digress. A habit, in general, plays out as follows:

Cue -> Routine -> Reward

This may appear trivial when thinking about the kind of everyday habits we’re normally concerned with – biting our nails, having a coffee, checking snapstagram, etc. – but it could have non-obvious things to say about problem solving. For example, when a teacher is presented with a problem they are quickly, as if without thinking, to get the correct answer. This unthinking aspect suggests to me that at least partially there is some element of habitual reasoning going on. For example, if I’m presented with the following:

What is the gradient at x=2?

My brain seems to do the following things without much effort: 1. notices “f(x)”, 2. notices “gradient”, 3.notices “at x=2”. These three things combined are sufficient to cue the routine for differentiation in order to find the gradient. My question is:

Would thinking in terms of habits be of use to students?

An immediate objection to this idea might be that maths is an odd subject and that the other subjects are more complex and less formulaic. This may be true in general but there may be parts of subjects like English or Classical Studies that could make use of this framework: for example, writing an essay is incredibly formulaic. A better objection may be to ask whether thinking in terms of habits for these subjects may be more of a hindrance than a help.

A different kind of objection could be that this is exactly the kind of practice teachers have been trying to disentangle themselves from for decades: namely, rote learning. Terror! Woe! Maybe not. There does seem to be evidence suggesting a middle ground memorisation and general strategies is the best way forward (more on this at a later date, I would imagine). Regardless, this is going to occupy my thinking for the next wee while.

In an effort to give it some semblance of scrutiny I’ll be breaking it down into three stages: Routine, Cue, and Reward (shockingly enough), in that order.

Routine – I’ll look at Mastery as a means for building the skills.

Cue – I’ll look at language: breaking down what each word means and then building connections with the skills themselves.

Reward –I’m not sure yet, that’s Future-Rees’s problem.

Unfortunately it won’t have the benefit of a rigorous experiment but it should be interesting to see if we can put Kamaji to work in the classroom.